Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<bits/stdc++.h>

#define REP(i,s,n) for(int i=s;i<n;++i)
#define rep(i,n) REP(i,0,n)
#define EPS (1e-6)
#define equals(a,b) (fabs((a)-(b))<EPS)

using namespace std;

bool LT(double a,double b) { return !equals(a,b) && a < b; }
bool LTE(double a,double b) { return equals(a,b) || a < b; }

int n, a[1010];

int main() {
  cin >> n;
  rep(i,n) cin >> a[i];
  sort(a,a+n);
  double maxi = 0;
  rep(i,n) REP(j,i+1,n) {
    double C = a[j], D = a[i];
    double A,B;
    int k = n-1;
    vector<int> ps;
    while( ps.size() < 2 ) {
      assert( k >= 0 );
      if( k != i && k != j ) ps.push_back(k);
      --k;
    }
    A = a[ps[0]];
    B = a[ps[1]];
    maxi = max(maxi,(A+B)/(C-D));
  }
  printf("%.10f\n",maxi);
  return 0;
}